For which pair of function is (g*f)(a)=|a|-2 1. f(a)=a^2-4 and g(a)= sqaureroot a 2. f(a)= 1/2a-1 and g(a)=2a-2 3. f

Question

For which pair of function is (g*f)(a)=|a|-2

1. f(a)=a^2-4 and g(a)= sqaureroot a
2. f(a)= 1/2a-1 and g(a)=2a-2
3. f(a)=5+a^2 and g(a) = sqaureroot (a-5)-2
4.f(a) =3 -3a and g(a)=4a-5

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2022-06-28T00:37:30+00:00 2 Answers 0

Answers ( 2 )

  1. Ruby
    0
    2022-06-28T00:38:35+00:00
    Reply

    Answer:

    The correct pair is 3

    Step-by-step explanation:

    1.

    [tex]f(a)=a^{2}-4 , g(a)=sqrt{a} gof(a)=g(a^{2} -4)=sqrt{a^{2}-4 } neq |a|-2[/tex]

    2.

    [tex]f(a)=frac{1}{2cdot a-1}, g(a)=2cdot a -2gof(a)=g(frac{1}{2cdot a-1} )=frac{2}{2cdot a-1}-2=frac{4-2cdot a}{2cdot a-1}neq|a|-2[/tex]

    3.

    [tex]f(a)=5+a^{2} , g(a)=sqrt{a-5} -2gof(a)=g(5+a^{2} )=sqrt{5+a^{2}-5 } -2=sqrt{a^{2} } -2=|a|-2[/tex]

    4.

    [tex]f(a)=3-3cdot a , g(a)=4cdot a-5gof(a)=g(3-3cdot a )=4(3-3cdot a)-5=7-12cdot aneq|a|-2[/tex]

    Hence, the Option 3 is correct

  2. Ada125lyn
    0
    2022-06-28T00:39:26+00:00
    Reply

    None of the pairs will deliver (gxf)(a). If you intend (gu2218f)(a), then …

    … selection 3 is appropriate.

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